So I finally manned up and just went for it. As of April 2015, the OneDrive sync engine on Windows 8.1 is sophisticated enough to recognise the files, and avoid all of the issues I feared in the question. I clicked on the notification area icon, and clicked 'Resume synchronisation'. Whilst it started resuming, I copied the local files into the OneDrive folders, choosing to 'replace all' the not-downloaded OneDrive copies. After a moment, Windows realised they were the same files and didn't upload/duplicate them.
However, I did have some issues.
1) Because I had not synced OneDrive on that desktop for so long, when I clicked 'resume', it looked like nothing was happening. But rest assured that it is indeed syncing. There was no way to pause the sync whilst it was in the process of resuming.
2) I accidentally clicked 'make online only' on my OneDrive folder in the file explorer, whilst it was resuming syncing. Don't do this. This messed things up, causing some duplicates (with the name of the desktop computer suffixed to the filenames). Luckily, only a small proportion of files were duplicated. This resulted in, for example, a DSC_0001.jpg [the original, online-only, syncing] and a DSC_0001-brianPC.jpg [available offline, syncing]. If I tried to delete DSC_0001-brianPC.jpg and then re-replace DSC_0001.jpg with the local version, it had to re-upload DSC_0001.jpg unfortunately. So make sure not to click 'make online only'.
3) Before I started, I decided to run the OneDrive troubleshooter to reset OneDrive on that desktop. I thought OneDrive would start from square one again, on that desktop, but actually the OneDrive files and folders were unaffected. In fact, the sync resumed afterwards, earlier than I wanted. This didn't really matter in the end.
I suspect that one factor that can determine whether OneDrive will recognise (i.e. not duplicate) the files depends on the 'date modified' metadata. Wait, I don't think so actually. Perhaps it is more to do with which hard disk the files you are using to replace the OneDrive files are on. Or perhaps it just gets messed up if you accidentally make files online-only.